What about a doctor from a conjoined species? Two heads, each one has a different personality. Their species can have one head go dormant by mutual agreement while the other is awake. You never know whether you'll be treated by one, the other, or both when you go into sickbay. They don't always argue, but they have different approaches /ideas about a problem.
Well that would be very similar to Nuvo Auz, the illegally joined Trill. (Nuvo is a sleezeball ex drug-dealer and Auz, the symbiont, is a colossal snob, resulting in one confused entity.)
I'm thinking I'll make Charleston the doctor. Since Starfleet saved her life, she wants to return the favor, while also partaking in exploration. On her own planet she's regarded as something of a veterinarian for those cute little Humanoids.